Wavelength of Sodium Light by Spectrometer

Determination of sodium light wavelength using a plane diffraction grating and spectrometer; includes procedure, calculations, precautions, and viva questions.

Apparatus

A spectrometer, spirit level, sodium lamp, diffraction grating with clamping arrangement, and eyepiece.

Observations and Calculations

Least count of the spectrometer:
Value of the smallest scale division / Number of divisions on the Vernier scale

No. of lines ruled on the grating:
15000/inch = 15000/2.54 cm
Grating element (a+b): 2.54/15000 cm

Order of spectrum(n)	Vernier	Reading for			Angle of diffraction				Wavelength
		Left	Direct	Right	Left	Right	Mean
1 2

Result:
The wavelength of sodium light = ______ Å (1 Å = 10⁻⁸ cm)

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Procedure

First, focus the eyepiece on the cross-wires and adjust both the telescope and collimator for parallel rays of light. Then, level the prism table using the spirit level. Afterward, make other necessary adjustments to the spectrometer.

Next, make the slit of the collimator narrow and symmetrical with respect to the telescope cross-wires. Find the Vernier constant and record readings of both Verniers against the circular scale.

Now, turn the telescope 90° to the left and fix it. Place the grating on the prism table so that it is perpendicular to the line joining two leveling screws (L and N). Allow light from the collimator to fall on the plane side of the grating. Rotate the table until the reflected light from the grating aligns with the telescope cross-wires. At this stage, the grating makes an angle of 45° with the telescope axis.

After alignment, ensure the image of the slit is symmetrical. If not, adjust screws N and L carefully. Then, rotate the table an additional 45° so the grating is perpendicular to the incoming light. Fix the table and release the telescope.

Gradually turn the telescope to the left until the image of the slit appears — this is the first-order spectrum. Adjust the cross-wire to align with the left edge of the yellow line and record the position (OA₁). Similarly, measure the right side (OB) and calculate the angle of diffraction.

Repeat the same process for the second-order spectrum.
Use the formula:

$$(a+b)\sin \theta =n\lambda$$

where

• $n=1,2,\dots$ (order of spectrum)

• $a+b$ = grating element

• $\theta$ = angle of diffraction

• $\lambda$ = wavelength of sodium light

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Precautions

• The grating should be placed vertically.

• Avoid touching the ruled surface of the grating.

• Ensure all spectrometer adjustments are accurate.

• The ruled surface should face toward the observer.

• The light should cover the entire grating surface.

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Viva Voce

Q1. What type of spectrum is obtained with a grating?
Ans. It is a normal spectrum.

Q2. Define diffraction of light.
Ans. The bending of light around sharp corners and edges is called diffraction.

Q3. What is a grating element?
Ans. On a grating, the width of spacing is denoted by a and that of rulings by b, and (a+b) is called the grating element.

Q4. What is the difference between interference and diffraction fringes?
Ans. Interference fringes are equally spaced, while diffraction fringes are not equally spaced.